92d EXAMPLE BLACK BODY RADIATION AND STIMULATED EMISSION 2 E2 3 2 eV An ensemble of 2 level atoms is located 10 cm from a spherical blackbody radiator 1 cm in diameter What is the rate of stimulated emission of the atoms A21 106 s 1 h 108 s 1 E1 0 1 cm atoms m 1 10 1 dN2 N 2 dt A 21 B21 1c Blackbody radiator TB 5000 K Photon h E 2 E1 19 J eV 3 2 eV 1 6 10 E E 2n 1 6 63 10 34 J s 7 72 1014 s 1 10 c 3 10 cm s 3885 7 72 1014 s 1 Black Body Power Flux at Surface of Radiator 3 1 J 0 0 c 8 h2 2 h exp KT 1 cm s Hz c 8 6 63 10 34 7 72 1014 3 J s s2 34 2 3 7 72 1014 3 1010 2 exp 6 63 10 23 1 s cm 1 38 10 5000 5 12 10 12 J cm 2 s Hz Black Body Power Flux at Atoms r2 body 0 2 5 12 10 12 2 J 0 5 10 cm s Hz ratoms 1 28 10 2 14 W cm Hz 2 92e Black Body Energy Density at Atoms 1 28 10 14 J 10 2 c 3 10 cm s Hz 4 26 10 25 J cm Hz 3 8 33 10 7 photons Photon 3 2 eV 1 6 10 19 J cm 3 Hz eV Stimulated Emission Coefficient 6 8 3 cm3 B21 A 21 10 3885 10 8 h 8 6 63 10 34 s J s 3 3 52 1024 cm2 J s 3 2 eV 1 6 10 19 Photon J eV 6 1 80 10 Photon cm3 s2 Stimulated Emission Rate 1 dN2 B 3 52 1024 4 21 10 25 cm3 J s 21 N 2 dt J s2 cm3 1 499 s 1 The NATURAL radiative relaxation rate is 106 s 1 so stimulated emission is negligible only 10 5 that of spontaneous emission 92f EXAMPLE STIMULATED EMISSION BY AN Ar LASER Same conditions as the black body radiator example What is the rate of stimulated emission 2 E2 3 2 eV 1 mm Laser 1 Watt laser 108 s 1 A21 106 s 1 E1 0 1 Note Total power radiated by black body at all wavelengths 4 2 P T 4 rb 12 W 4 2 5 67 10 5000 4 0 5 cm 11 1 kW 4 2 K cm Power Flux P 1 photon 1W 19 photons W 127 3 8 65 10 0 1 cm 2 J cm2 s cm2 3 2 eV 1 6 10 19 eV 4 Photon Energy Density J s 127 3 J P 4 24 10 17 3 c cm2 s cm Hz 108 3 1010 cm Hz 82 9 Photons 3 cm Hz Rate of Stimulated Emission 1 dN2 B 1 80 106 82 9 Photon cm 3 s 21 N 2 dt Photon cm 3 s2 1 49 10 8 s 1 A 21 106 s 1 For a much lower power 1 W vs 11 1 kW stimulated emission with the laser is much greater than natural radiative relaxation Compared to the black body radiator the laser has more photons in the bandwidth of the atomic transition